function kap_return = KAPPA5(a, b, c, d, e, x0)  
    kap_return = zeros(size(x0));  
    y_prime = @(x) 5*a*x.^4 + 4*b*x.^3 + 3*c*x.^2 + 2*d*x + e;  
    y_double_prime = @(x) 20*a*x.^3 + 12*b*x.^2 + 6*c*x + 2*d;  
    for i = 1:length(x0)  
        x = x0(i);  
        y_prime_value = y_prime(x);  
        y_double_prime_value = y_double_prime(x);  
        kap_return(i) = abs(y_double_prime_value) / ((1 + y_prime_value^2)^(3/2));  
    end  
end
